Monoidal Category Research Articles

Numerical simulation and improvement of combustor structure in 3D printed sand recycling system

Abstract In this paper, a new combustor with an output of 5 t/h is designed based on a computational particle fluid dynamics (CPFD) model. The flow field simulation is combined with the combustion simulation to analyze the internal two-phase flow, temperature field, and combustion products. The combustor structure was optimized. The simulation results show that the recovery efficiency of the waste sand and the energy utilization of the combustor can be improved under the original structure. The sand bed has a significant effect on flow field characteristics. The increase in particle temperature in the combustor increases the efficiency of waste sand recovery by increasing the height of the sand bed by 50 mm. The utilization rate of natural gas is increased and the economic efficiency is improved. The feasibility of the CPFD method can simulate the flow field characteristics inside the combustor very effectively.

Stable Acoustic Pulling in Two-Dimensional Phononic Crystal Waveguides Based on Mode Manipulation

Acoustic manipulation is a set of versatile platforms with excellent manipulation capabilities. In recent years, researchers have increasingly achieved specific manipulations beyond the translation and capture of particles. Here, we focus on the acoustic field momentum mechanism that generates an acoustic radiation force (ARF). A phononic crystal (PC) waveguide is established to amplify the forward momentum of the acoustic beam through the mode conversion of the acoustic field. Based on the conservation of momentum, the object gains reverse momentum. Thus, acoustic pulling can be achieved through the mode conversion of the acoustic field. Furthermore, we analyze the ARFs of two identical objects. It turns out that they can be manipulated separately by opposing forces. Our study provides a new way to achieve stable long-range acoustic pulling, and will explore, beneficially, the interaction between acoustic waves and matter.

On the spectrum and support theory of a finite tensor category

On the spectrum and support theory of a finite tensor category

Evaluation of internal teat sealant persistence in the mammary gland during the dry period

The aim of this study was to characterize the behavior of 2 commercially available internal teat sealants containing bismuth subnitrate (SOa and ORBb) during the dry- and postfresh periods in dairy cattle. Digital radiography was used to monitor location and percentage of teat cistern fill at dry-off and during the dry period. Teat-level health parameters including infection status at dry-off and post-fresh as well as incidence of clinical mastitis were also assessed. Radiographic imaging revealed that 21.1% of teats had sealant present in the gland cistern at dry-off (SO= 23.6%, ORB = 18.5%) which increased to 55.9% (SO = 59.6%, ORB = 52.2%) at pre-fresh imaging. Quarters with sealant that had migrated into the gland shed noticeable amounts of sealant for twice as long (mean 14.34 milkings), compared to quarters that did not have sealant in the gland (mean: 7.12, P < 0.001). There was no correlation between sealant location and intramammary infection at dry-off or post-fresh, nor did sea ant location impact clinical mastitis in the first 120 days in milk. Milk leakage after dry-off also was not correlated with an increased risk of intramammary infection during the dry or post-fresh periods. There was no difference between treatments in any of the parameters evaluated. Prolonged sealant shedding is a common reason that producers cite for not utilizing internal teat sealant products in their dry-off protocols. Further research is indicated to determine the optimal amount of sealant required to provide protection while minimizing post-fresh shedding.

Nilpotent Category of Monoidal Category and Tensor–Hom Adjunction

Nilpotent Category of Monoidal Category and Tensor–Hom Adjunction

Genuine versus naïve symmetric monoidal $G$-categories

We prove that through the eyes of equivariant weak equivalences the genuine symmetric monoidal G -categories of Guillou and May [Algebr. Geom. Topol. 17 (2017), no. 6, 3259–3339] are equivalent to just ordinary symmetric monoidal categories with G -action. Along the way, we give an operadic model of global infinite loop spaces and provide an equivalence between the equivariant category theory of genuine symmetric monoidal G -categories and the G -parsummable categories studied by Schwede [J. Topol. 15 (2022), no. 3, 1325–1454] and the author [New York J. Math. 29 (2023), 635–686].

Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras

Let g be a complex simple Lie algebra and UqLg the corresponding quantum affine algebra. We construct a functor Fθ between finite-dimensional modules over a quantum symmetric pair subalgebra of affine type Uqk⊂UqLg and an orientifold KLR algebra arising from a framed quiver with a contravariant involution, providing a boundary analogue of the Kang-Kashiwara-Kim-Oh generalized Schur-Weyl duality. With respect to their construction, our combinatorial model is further enriched with the poles of a trigonometric K-matrix intertwining the action of Uqk on finite-dimensional UqLg-modules. By construction, Fθ is naturally compatible with the Kang-Kashiwara-Kim-Oh functor in that, while the latter is a functor of monoidal categories, Fθ is a functor of module categories. Relying on a suitable isomorphism à la Brundan-Kleshchev-Rouquier, we prove that Fθ recovers the Schur-Weyl dualities due to Fan-Lai-Li-Luo-Wang-Watanabe in quasi-split type AIII.

Path integration, rather than being suppressed, is used to update spatial views in familiar environments with constantly available landmarks

This project tested three hypotheses conceptualizing the interaction between path integration based on self-motion and piloting based on landmarks in a familiar environment with persistent landmarks. The first hypothesis posits that path integration functions automatically, as in environments lacking persistent landmarks (environment-independent hypothesis). The second hypothesis suggests that persistent landmarks suppress path integration (suppression hypothesis). The third hypothesis proposes that path integration updates the spatial views of the environment (updating-spatial-views hypothesis). Participants learned a specific object's location. Subsequently, they undertook an outbound path originating from the object and then indicated the object's location (homing). In Experiments 1&1b, there were landmarks throughout the first 9 trials. On some later trials, the landmarks were presented during the outbound path but unexpectedly removed during homing (catch trials). On the last trials, there were no landmarks throughout (baseline trials). Experiments 2–3 were similar but added two identical objects (the original one and a rotated distractor) during homing on the catch and baseline trials. Experiment 4 replaced two identical objects with two groups of landmarks. The results showed that in Experiments 1&1b, homing angular error on the first catch trial was significantly larger than the matched baseline trial, undermining the environment-independent hypothesis. Conversely, in Experiment 2–4, the proportion of participants who recognized the original object or landmarks was similar between the first catch and the matched baseline trial, favoring the updating-spatial-views hypothesis over the suppression hypothesis. Therefore, while mismatches between updated spatial views and actual views of unexpected removal of landmarks impair homing performance, the updated spatial views help eliminate ambiguous targets or landmarks within the familiar environment.

Tensor category [formula omitted] via minimal affine W-algebras at the non-admissible level [formula omitted

We prove that the Kazhdan-Lusztig category of slˆm at level k, KLk(slm), is a semi-simple, rigid braided tensor category for all even m≥4, and k=−m+12. Moreover, all modules in KLk(slm) are simple-currents and they appear in the decomposition of conformal embeddings glm↪slm+1 at level k=−m+12. For this we inductively identify minimal affine W-algebra Wk−1(slm+2,θ) as simple current extension of Lk(slm)⊗H⊗M, where H is the rank one Heisenberg vertex algebra, and M the singlet vertex algebra for c=−2. The proof uses previously obtained results for the tensor categories of singlet algebra. We also classify all irreducible ordinary modules for Wk−1(slm+2,θ). The semi-simple part of the category of Wk−1(slm+2,θ)–modules comes from KLk−1(slm+2), using quantum Hamiltonian reduction, but this W-algebra also contains indecomposable ordinary modules.

Asymptotics in finite monoidal categories

We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.

Types of Polymers Using in 3D Printing and Their Applications: A Brief Review

The technology based on using 3D printing machines (3DPs) can be considered a promising approach in industry. A 3D printer might be define as machines which manufacture 3D products or models that already designed by computer aided design (CAD) software programs. These machines can create geometries that are very complicated and so difficult to fabricate by traditional manufacturing approaches. Additionally, it has capability to create items that is so complex internal design products with lower time and cost. Several kinds of materials have been applied in this technology. The polymers is one the most common materials that are using in 3D printing. This review seeks to clarify the features and benefits of different types of polymers including Acrylonitrile Butadiene Styrene (ABS), Polylactic acid (PLA), Acrylonitrile styrene acrylate (ASA), Polyethylene terephthalate (PET), Glycolized polyester(PETG), Polycarbonate (PC), Polypropylene (PP), Nylon, and Hybrid and composite materials.

Traced Monads and Hopf Monads

A traced monad is a monad on a traced symmetric monoidal category that lifts the traced symmetric monoidal structure to its Eilenberg-Moore category. A long-standing question has been to provide a characterization of traced monads without explicitly mentioning the Eilenberg-Moore category. On the other hand, a symmetric Hopf monad is a symmetric bimonad whose fusion operators are invertible. For compact closed categories, symmetric Hopf monads are precisely the kind of monads that lift the compact closed structure to their Eilenberg-Moore categories. Since compact closed categories and traced symmetric monoidal categories are closely related, it is a natural question to ask what is the relationship between Hopf monads and traced monads. In this paper, we introduce trace-coherent Hopf monads on traced monoidal categories, which can be characterized without mentioning the Eilenberg-Moore category. The main theorem of this paper is that a symmetric Hopf monad is a traced monad if and only if it is a trace-coherent Hopf monad. We provide many examples of trace-coherent Hopf monads, such as those induced by cocommutative Hopf algebras or any symmetric Hopf monad on a compact closed category. We also explain how for traced Cartesian monoidal categories, trace-coherent Hopf monads can be expressed using the Conway operator, while for traced coCartesian monoidal categories, any trace-coherent Hopf monad is an idempotent monad. We also provide separating examples of traced monads that are not Hopf monads, as well as symmetric Hopf monads that are not trace-coherent.

INTERCULTURALITY AND ITS LINGUISTIC CONSIDERATION: THREE PARADIGMS

: This article is based on the understanding that language is highly complex and has a cognitive, cultural, and formal component. Within this framework, the focus is on the network of relationships regulated by multiple perspectives between culture and language (both as system and as usage), particularly considering the multifaceted term “interculturality”. First, in order to establish a common ground, I provide an overview of the different concepts of the interaction between language and culture in the linguistic research discourse. Furthermore, an overview of the various culture-sensitive linguistic analytical approaches will be developed. In the main body, three recent paradigms, each of different provenance, will be critically presented and compared regarding their content-related concept and their performance potential. These are (a) Russian and post-Soviet “Linguoculturology” (LC), (b) Anglophone “Cultural Linguistics” (CL), and (c) “Intercultural Linguistics” (IL), primarily origininating in German Studies with a particular focus on multilingualism. It becomes apparent that LC investigates the influence of language on culture, whereas CL aims its attention at the influence of culture on language, while in IL, multi-culturality as well as inter- and transculturality are the focal point. The presented paradigms differ significantly with regard to their respective underlying understanding of culture and their disciplinary orientation: LC and CL exhibit a distinctive cognitive orientation, whereas IL is more based on Contrastive Linguistics and Cultural Studies. The conducted analysis gives evidence of the isolated development of all three schools of thought, especially LC and CL, despite their almost identical research objectives.

Prime representations in the Hernandez–Leclerc category: classical decompositions

Abstract We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez–Leclerc (HL) category for the quantum affine algebra associated with $\mathfrak {sl}_{n+1}$ . When the HL category is realized as a monoidal categorification of a cluster algebra (Hernandez and Leclerc (2010, Duke Mathematical Journal 154, 265–341); Hernandez and Leclerc (2013, Symmetries, integrable systems and representations, 175–193)), these representations correspond precisely to the cluster variables and the frozen variables are minimal affinizations. For any height function, we determine the classical decomposition of these representations with respect to the Hopf subalgebra $\mathbf {U}_q(\mathfrak {sl}_{n+1})$ and describe the graded multiplicities of their graded limits in terms of lattice points of convex polytopes. Combined with Brito, Chari, and Moura (2018, Journal of the Institute of Mathematics of Jussieu 17, 75–105), we obtain the graded decomposition of stable prime Demazure modules in level two integrable highest weight representations of the corresponding affine Lie algebra.

Dilations and information flow axioms in categorical probability

AbstractWe study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity, but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation.

What's next?: Time is subjectively dilated not only for 'oddball' events, but also for events immediately after oddballs.

Our experience of time is strikingly plastic: Depending on contextual factors, the same objective duration can seem to fly by or drag on. Perhaps the most direct demonstration of such subjective time dilation is the oddball effect: when seeing identical objects appear one after another, followed by an "oddball" (e.g., a disc that suddenly grows in size, in a sequence of otherwise static discs), observers experience this oddball as having lasted longer than its nonoddball counterparts. Despite extensive work on this phenomenon, a surprisingly foundational question remains unasked: What actually gets dilated? Beyond the oddball, are the objects just before (or just after) the oddball also dilated? As in previous studies, observers viewed sequences of colored discs, one of which could be the oddball-and subsequently reproduced the oddball's duration. Unlike previous studies, however, there were also critical trials in which observers instead reproduced the duration of the disc immediately before or after the oddball. A clear pattern emerged: oddball-induced time dilation extended to the post-oddball disc, but not the pre-oddball disc. Whence this temporal asymmetry? We suggest that an oddball's sudden appearance may induce uncertainty about what will happen next, heightening attention until after the uncertainty is resolved.

The 5-HT1A receptor agonist 8-OH-DPAT modulates motor/exploratory activity, recognition memory and dopamine transporter binding in the dorsal and ventral striatum

In the present studies, we assessed the effect of the 5-HT1A receptor (R) agonist 8-hydroxy-2-(di-n-propylamino)tetralin (8-OH-DPAT) on motor and exploratory behaviors, object and place recognition and dopamine transporter (DAT) and serotonin transporter (SERT) binding in the rat brain. In Experiment I, motor/exploratory behaviors were assessed in an open field after injection of either 8-OH-DPAT (0.1 and 3 mg/kg) or vehicle for 30 min without previous habituation to the open field. In Experiment II, rats underwent a 5-min exploration trial in an open field with two identical objects. After injection of either 8-OH-DPAT (0.1 and 3 mg/kg) or vehicle, rats underwent a 5-min test trial with one of the objects replaced by a novel one and the other object transferred to a novel place. Subsequently, N-o-fluoropropyl-2b-carbomethoxy-3b-(4-[123I]iodophenyl)-nortropane ([123I]FP-CIT; 11 ± 4 MBq) was injected into the tail vein. Regional radioactivity accumulations were determined post mortem with a well counter. In both experiments, 8-OH-DPAT dose-dependently increased ambulation and exploratory head-shoulder motility, whereas rearing was dose-dependently decreased. In the test rial of Experiment II, there were no effects of 8-OH-DPAT on overall activity, sitting and grooming. 8-OH-DPAT dose-dependently impaired recognition of object and place. 8-OH-DPAT (3 mg/kg) increased DAT binding in the dorsal striatum relative to both vehicle and 0.1 mg/kg 8-OH-DPAT. Furthermore, in the ventral striatum, DAT binding was decreased after 3 mg/kg 8-OH-DPAT relative to vehicle. Findings indicate that motor/exploratory behaviors, memory for object and place and regional dopamine function may be modulated by the 5-HT1AR. Since, after 8-OH-DPAT, rats exhibited more horizontal and less (exploratory) vertical motor activity, while overall activity was not different between groups, it may be inferred, that the observed impairment of object recognition was not related to a decrease of motor activity as such, but to a decrease of intrinsic motivation, attention and/or awareness, which are relevant accessories of learning. Furthermore, the present findings on 8-OH-DPAT action indicate associations not only between motor/exploratory behavior and the recognition of object and place but also between the respective parameters and the levels of available DA in dorsal and ventral striatum.

A linear exponential comonad in s-finite transition kernels and probabilistic coherent spaces

This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonad arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions.A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.

The twisted tensor product of dg categories and a contractible 2-operad

It is well-known that the “pre-2-category” Catdgcoh(k) of small dg categories over a field k, with 1-morphisms defined as dg functors, and 2-morphisms defined as the complexes of coherent natural transformations, fails to be a strict 2-category. The question “What do dg categories form?”, raised by V. Drinfeld in [14], is interpreted in this context as a question of finding a weak 2-category structure on Catdgcoh(k). In [32], D. Tamarkin proposed an answer to this question, by constructing a contractible 2-operad in the sense of M. Batanin [3], acting on Catdgcoh(k).In this paper, we construct another contractible 2-operad, acting on Catdgcoh(k). Our main tool is the twisted tensor product of small dg categories, introduced in [25]. We establish a one-side associativity for the twisted tensor product, making (Catdgcoh(k),⊗∼) a skew monoidal category in the sense of [30], and construct a twisted compositionCohdg(D,E)⊗∼Cohdg(C,D)→Cohdg(C,E), and prove some compatibility between these two structures. Taken together, the two structures give rise to a 2-operad O, acting on Catdgcoh(k). Its contractibility is a consequence of a general result of [25].

Teaching Receptive Vocabulary to Minimally Verbal Preschoolers With Autism Spectrum Disorder: A Single-Case Multiple Baseline Design.

The purpose of this multiple probe design was (a) to investigate whether the use of the match-to-sample (MtS) procedure would result in independent identification of objects and (b) to examine whether the participants could generalize to matching objects and nonidentical pictures. Using a nonconcurrent multiple baseline design, three minimally verbal preschoolers with autism spectrum disorder and receptive language impairment were taught to identify common objects using a MtS procedure and physical prompts. Participants were taught to match identical objects to identical pictures. Maintenance checks were completed following mastery of vocabulary for a total of 22 words. Generalization probes were conducted with the objects and nonidentical pictures. Intervention was completed by a speech-language pathologist during typical speech-language pathology sessions. Results illustrated that all of the participants learned to match and generalize the pictures. All were able to independently identify the objects at 1-month follow-up. MtS and prompting appear to be effective procedures for teaching receptive vocabulary and can be easily implemented by education professionals. Learner profiles varied for the participants in this study and are an important aspect when teaching students with autism spectrum disorder and co-occurring receptive language impairment.